ES226 SPRING 2018 Lesson 21 – 3D Rigid-Body Equilibrium

“I went undefeated for seven years, lost a match, and then I got good.” – Dan Gable LESSON 21 – 3D RIGID-BODY EQUILIBRIUM

Monday, February 26, 2018 LESSON OBJECTIVES

1. Identify the force and moment reaction components on a 3D rigid free body, including (but not limited to): smooth supports, roller supports, link supports, cable supports, pin supports, fixed supports.

2. Identify cases in which support moment couples are known to be zero because of “properly aligned bearings.” 3. Draw free body diagrams for 3D rigid bodies, labeling all external forces and moments, known or unknown. 4. Solve the unknown reactions of 3D free bodies, using up to six equations of equilibrium.

REQUIRED READING Hibbeler Chapter 5: 5.6, 5.7

SUPPORTS AND UNKNOWNS UP TO 6 UNKNOWNS AT A SUPPORT (3 FORCES, 3 MOMENTS) ANYTHING THAT IS “FREE” IS NOT UNKNOWN (CORRESPONDING FORCE OR MOMENT IS ZERO).

WHAT IS FREE (TO MOVE OR ROTATE)?

z

x y

z

x y

z

x y

z

x y

Fx Fy Fz Mx My Mz

Fx Fy Fz Mx My Mz

Fx Fy Fz Mx My Mz

Fx Fy Fz Mx My Mz

ES226 SPRING 2018 Lesson 21 – 3D Rigid-Body Equilibrium

FEWER UNKNOWNS DUE TO “PROPERLY ALIGNED BEARINGS” (LABEL UNKNOWN

REACTIONS)

DOOR WITH 1 HINGE DOOR WITH 2 HINGES

z

x y

z

x

y

Fx Fy Fz Mx My Mz

Fx Fy Fz Mx My Mz

ES226 SPRING 2018 Lesson 21 – 3D Rigid-Body Equilibrium

IN-CLASS PROBLEMS:

1.

2.

ES226 SPRING 2018 Lesson 21 – 3D Rigid-Body Equilibrium

Homework (Due Wednesday). 1. Determine the tension in the cable and the reactions at A and B if =45°. Given: the 250x400-mm plate has a mass of

12 kg; a 300-mm-diameter pulley is welded to axle AC, which is supported by aligned journal bearings A and B.

2. The uniform concrete slab has a weight of 5500 lb. Determine the tension in each of the three parallel supporting cables

when the slab is held in the horizontal plane as shown.

3. Member AB is supported by a cable BC and at A by a SQUARE rod which fits loosely through the square hole at the

end joint of the member as shown. Determine the components of reaction at A and the tension in the cable needed to hold the 800-lb cylinder in equilibrium.